A $5000\, kg$ rocket is set for vertical firing. The exhaust speed is $800\,m{s^{ - 1}}$. To give an initial upward acceleration of $20\,m{s^{ - 2}}$, the amount of gas ejected per second to supply the needed thrust will be ........... $kg\,{s^{ - 1}}$ $(g = 10\,m{s^{ - 2}})$
A $5000\, kg$ rocket is set for vertical firing. The exhaust speed is $800\,m{s^{ - 1}}$. To give an initial upward acceleration of $20\,m{s^{ - 2}}$, the amount of gas ejected per second to supply the needed thrust will be ........... $kg\,{s^{ - 1}}$ $(g = 10\,m{s^{ - 2}})$
$127.5$
$187.5$
$185.5$
$137.5$
A $5000\, kg$ rocket is set for vertical firing. The exhaust speed is $800\,m{s^{ - 1}}$. To give an initial upward acceleration of $20\,m{s^{ - 2}}$, the amount of gas ejected per second to supply the needed thrust will be ........... $kg\,{s^{ - 1}}$ $(g = 10\,m{s^{ - 2}})$
$F = \frac{{u\,dm}}{{dt}} = m(g + a)$
$⇒$ $\frac{{dm}}{{dt}} = \frac{{m(g + a)}}{u}$ $ = \frac{{5000 \times (10 + 20)}}{{800}}$ $ = 187.5\;kg/s$
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